Subcritical core reactivity bias projection technique

ABSTRACT

A method to determine a global core reactivity bias and the corresponding estimated critical conditions of a nuclear reactor core prior to achieving reactor criticality. The method first requires collection and evaluation of the inverse count rate ratio (ICRR) data; specifically, fitting measured ICRR vs. predicted ICRR data. The global core reactivity bias is then determined as the amount of uniform reactivity adjustment to the prediction that produces an ideal comparison between the measurement and the prediction.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application claims the priority benefit under 35 U.S.C. §119(e) of U.S. Provisional Application No. 62/597,571 filed on Dec. 12,2017, the contents of which are herein incorporated by reference.

BACKGROUND 1. Field

The disclosed concept relates generally to methods for predicting when anuclear reactor core will go critical and, more specifically, to amethod for determining a global core reactivity bias and thecorresponding estimated critical conditions of a nuclear reactor coreprior to achieving reactor criticality.

2. Related Art

In a pressurized water reactor power generating system, heat isgenerated within the core of a pressure vessel by a fission chainreaction occurring in a plurality of fuel rods supported within thecore. The fuel rods are maintained in a spaced relationship within fuelassemblies with the space between fuel rods forming coolant channelsthrough which borated water flows. Hydrogen within the coolant watermoderates the neutrons emitted from enriched uranium within the fuelrods to increase the number of nuclear reactions and thus increase theefficiency of the process. Control rod guide thimbles are interspersedwithin the fuel assemblies in place of fuel rod locations and serve toguide control rods which are operable to be inserted or withdrawn fromthe core. When inserted, the control rods absorb neutrons and thusreduce the number of nuclear reactions and the amount of heat generatedwithin the core. Coolant flows through the assemblies out of the reactorto the tube side of steam generators where heat is transferred to waterin the shell side of the steam generators at a lower pressure, whichresults in the generation of steam used to drive a turbine. The coolantexiting the tube side of the steam generator is driven by a main coolantpump back to the reactor in a closed loop cycle to renew the process.

The power level of a nuclear reactor is generally divided into threeranges: the source or startup range, the intermediate range, and thepower range. The power level of the reactor is continuously monitored toassure safe operation. Such monitoring is typically conducted by meansof neutron detectors placed outside and inside the reactor core formeasuring the neutron flux of the reactor. Since the neutron flux in thereactor at any point is proportional to the fission rate, the neutronflux is also proportional to the power level.

Fission and ionization chambers have been used to measure flux in thesource, intermediate, and power range of a reactor. Typical fission andionization chambers are capable of operating at all normal power levels;however, they are generally not sensitive enough to accurately detectlow level neutron flux emitted in the source range. Thus, separate lowlevel source range detectors are typically used to monitor neutron fluxwhen the power level of the reactor is in the source range.

The fission reactions within the core occur when free neutrons at theproper energy level strike the atoms of the fissionable materialcontained within the fuel rods. The reactions result in the release of alarge amount of heat energy which is extracted from the core in thereactor coolant and in the release of additional free neutrons which areavailable to produce more fission reactions. Some of these releasedneutrons escape the core or are absorbed by neutron absorbers, e.g.,control rods, and therefore do not cause traditional fission reactions.By controlling the amount of neutron absorbent material present in thecore, the rate of fission can be controlled. There are always randomfission reactions occurring in the fissionable material, but when thecore is shut down, the released neutrons are absorbed at such a highrate that a sustained series of reactions do not occur. By reducing theneutron absorbent material until the number of neutrons in a givengeneration equals the number neutrons in the previous generation, theprocess becomes a self-sustaining chain reaction and the reactor is saidto be “critical”. When the reactor is critical, the neutron flux is sixor so orders of magnitude higher than when the reactor is shut down. Insome reactors, in order to accelerate the increase in neutron flux inthe shutdown core to achieve practical transition intervals, anartificial neutron source is implanted in the reactor core among thefuel rods containing the fissionable material. This artificial neutronsource creates a localized increase in the neutron flux to aid inbringing the reactor up to power.

In the absence of a neutron source, the ratio of the number of freeneutrons in one generation to those in the previous generation isreferred to as the “neutron multiplication factor” (K_(eff)) and is usedas a measure of the reactivity of the reactor. In other words, themeasure of criticality for a nuclear core is K_(eff), that is, the ratioof neutron production to total neutron loss contributable to bothdestruction and loss. When K_(eff) is greater than 1, more neutrons arebeing produced than are being destroyed. Similarly, when K_(eff) is lessthan one, more neutrons are being destroyed than are being produced.When K_(eff) is less than one, the reactor is referred to as being“subcritical”. Until relatively recently, there has been no directmethod for measuring when criticality will occur from the source rangeexcore detectors. Plant operators typically estimate when criticalitywill occur through a number of methods. One method for estimating whencriticality will occur is made by plotting the inverse ratio of thecount rate obtained from the source range detector as a function of thechange in conditions being used to bring the plant critical, e.g.,withdrawal of the control rods. When the plant goes critical, the sourcerange count rate approaches infinity and hence, the Inverse Count RateRatio (ICRR) goes to zero. Due to the physics of the reaction occurringwithin the core of the reactor, the ICRR curve is almost never linear.The control rod position changes have a significant impact on the shapeof the ICRR curve. Therefore, estimating the conditions under which theplant will go critical from the ICRR curve is subject to muchuncertainty, but also subject to considerable scrutiny by the UnitedStates Nuclear Regulatory Commission and Institute of Nuclear PowerOperations.

More recently, a method has been devised for directly predicting whenthe reactor will go critical. The method is described in U.S. Pat. No.6,801,593. In accordance with the method, the reactivity of the core isincreased while monitoring an output of a source range detector. Acorrection factor linearizes the ICRR so that the curve can bepredictably extrapolated. The method thus describes a spatiallycorrected inverse count rate core reactivity measurement process.However, this method does not address the accuracy of the corereactivity measurement, which is dependent on the accuracy of themeasured neutron radiation levels. In particular, it is very importantthat incremental changes in the measured neutron levels are determinedaccurately. The largest neutron measurement error component in aproperly operating neutron radiation detector is typically caused bywhat is commonly called a “background signal”. The background signalinduces a response in the detector measurement that is not caused bysource neutrons. This results in errors in the measured core reactivitychanges. In order to improve the accuracy of the neutron populationmeasurement, and obtain a corresponding improvement in accuracy in theICRR reactivity measurement process, it is necessary to remove anysignificant background signal component from the measurement before themeasurement is used to calculate the reactivity change. Prior to U.S.Pat. No. 7,894,565, there has been no direct method of determining thebackground signal content in a neutron signal measurement from thetypical neutron detectors used in commercial nuclear power facilities.U.S. Pat. No. 7,894,565 provides one such method, but there is stillroom for improving the estimate when the core will go critical.Additionally, currently a need exists for a method that can determine ifthe core is performing as designed and whether anomalies exist, beforethe core goes critical. Currently, such an analysis can only beperformed after the core goes critical as part of the low power physicstesting process, which has to be successfully concluded before thereactor is brought up to full power.

SUMMARY

The disclosed concept provides a method of determining the global corereactivity bias for a nuclear reactor core with a K_(eff) less than 1.The method comprises the step of measuring the subcritical neutron flux(i.e., measured neutron detector response) for one or more states of thereactor core. The method also includes the step of calculating aprediction of a spatially-corrected subcritical neutron flux (i.e.,predicted neutron detector response) for the one or more states of thereactor core. The method then determines a difference between themeasured and the predicted neutron detector response and records thedifference as the global core reactivity bias. In one embodiment of themethod, the measuring step is taken from the output of the source rangedetector and, preferably, the measuring, calculating and determiningsteps are performed under a plurality of steady-state subcriticalconditions, i.e. state points. Desirably, the plurality of steady-statesubcritical conditions are obtained by re-positioning the control rodswhile maintaining the other core conditions in steady-state.

The method may also include the step of using regression statistics ofthe measurements and predictions of the neutron detector response andapplying a quantitative measured-to-predicted criteria on the regressionstatistics to detect various core anomalies while the plant is in asubcritical condition and prior to the plant achieving criticality. Themethod may further include the step of determining the reactivity biasbetween a predicted core and an actual core (i.e., as-assembled corefollowing initial construction or refueling) by determining the uniformanalytical reactivity adjustment, which is the systematic globalreactivity bias, required to reconcile the measured neutron flux datawith the predicted neutron detector response.

The method may be carried out by a processing device programmed to carryout the method. Instructions for carrying out the method may be capturedon a machine readable medium for use by a processing device in carryingout the method.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the disclosed concept can be gained from thefollowing description of the preferred embodiments when read inconjunction with the accompanying drawings in which:

FIG. 1 is a schematic representation of the primary side of a nuclearpower generating system.

DESCRIPTION

FIG. 1 illustrates the primary side of a nuclear electric powergenerating plant 10 in which a nuclear steam supply system 12 suppliessteam for driving a turbine generator (not shown) to produce electricpower. The nuclear steam supply system 12 has a pressurized waterreactor 14 which includes a reactor core 16 housed within a pressurevessel 18. Fission reactions within the reactor core 16 generate heat,which is absorbed by a reactor coolant, light water, which is passedthrough the core. The heated coolant is circulated through hot legpiping 20 to a steam generator 22. Reactor coolant is returned to thereactor 14 from the steam generator 22 by a reactor coolant pump 24through cold leg piping 26. Typically, a pressurized water reactor hasat least two and often three or four steam generators 22 each suppliedwith heated coolant through a hot leg 20, which, along with the cold leg26 and reactor coolant pump 2 form a primary loop. Each primary loopsupplies steam to the turbine generator. One of such loops are shown inFIG. 1.

Coolant returned to the reactor 14 flows downward through an annulardowncomer, and then upward through the core 16. The reactivity of thecore, and therefore the power output of the reactor 14, is controlled ona short term basis by control rods, which may be selectively insertedinto the core. Long term reactivity is regulated through control of theconcentration of a neutron moderator such as boron dissolved in thecoolant. Regulation of the boron concentration affects reactivityuniformly throughout the core as the coolant circulates through theentire core. On the other hand, the control rods affect local reactivityand therefore, result in an asymmetry of the axial and radial powerdistribution within the core 16.

Conditions within the core 16 are monitored by several different sensorsystems. These systems include an excore detector system 28, whichmeasures neutron flux escaping from the reactor 14. The excore detectorsystem 28 includes source range detectors used when the reactor is shutdown, intermediate range detectors used during startup and shutdown, andpower range detectors used when the reactor is above approximately 5%power. Incore detectors are also typically employed during poweroperation; however, they are not relevant to this application.

Estimated critical conditions (ECC) are typically required as part ofany reactor startup evolution. ECC is a combination of control rod andprimary system conditions (e.g., soluble boron concentration, coolanttemperature) that are expected to yield a critical reactor state. It isvaluable, from a reactivity management perspective, that the ECC closelymatch the actual critical conditions of the core (i.e., the truecombination of control rod position and primary system conditions thatyield a critical reactor state). Furthermore, Plant TechnicalSpecifications include a limiting condition for operation (also referredto as LCO) that the core reactivity be measured within a specifiedamount of the predicted core reactivity. The associated surveillancesare performed prior to commencing power operation (typically >5% ratedthermal power) after each core refueling, and generally every monthafterward.

Various ECC combinations can be determined by nuclear design predictionsprior to reactor core operation. However, a more accurate ECC projectioncan be obtained through ICRR monitoring and evaluation prior to reactorcriticality, which can identify the presence of any global corereactivity bias. The global core reactivity bias is defined as thedifference between the predicted reactivity state of the core and theactual reactivity state of the core determined by measurement.Subsequently, the bias can be incorporated into an updated ECCprojection prior to reactor criticality.

ICRR monitoring is a common practice during shutdown/startup conditionsthat requires a baseline measurement from a neutron detector (M_(R)).Following a reactivity manipulation (e.g., control rod withdrawal) andachievement of a new steady state condition (state point), anothermeasurement is collected (M_(i)). The ratio of M_(R)/M_(i) is defined asthe ICRR for state point i. As additional reactivity manipulationsoccur, ICRR can be updated and monitored in terms of changes from thereference measurement, and in turn, how the reactor is progressingtowards (or away from) reactor criticality. If the intent is to startupthe reactor (i.e., bring the reactor to a critical state), positivereactivity is added to the core (e.g., control rod withdrawal, primarysystem soluble boron dilution), and the ICRR is expected to approachzero.

As described in U.S. Pat. No. 6,801,593, due to the physics of thereactions occurring within the reactor core, the ICRR is not linearunless the reactor is very close to criticality; control rod positionchanges as part of pre-critical testing and the approach to criticalityhave a significant impact on the shape of the ICRR curve. Therefore,U.S. Pat. No. 6,801,593 provided a means of linearizing the measuredICRR with changes in control rod position or core conditions.

The method described in U.S. Pat. No. 6,801,593 relied on use ofspatially-corrected ICRR (ICRR_(SC)) as the measurement parameter, whichis a function of neutron detector measurements (M_(R)/M_(i)), but isdependent on nuclear design by way of spatial correction factors (SCFs).U.S. Pat. No. 6,801,593 defined SCF as a function of the static spatialfactor and predicted eigenvalues obtained from subcritical, staticcalculations with and without fixed neutron sources.

Because ICRR_(SC) is partly dependent on design prediction, use ofICRR_(SC) as the primary measurement parameter is inherently subject tomasking effects, where an error or bias in the design prediction caninfluence the measurement as well. Hence, it is desirable from a reactorphysics measurement standpoint to eliminate predictive components frommeasurement results in order to eliminate the potential for maskingeffects. Therefore, the disclosed concept first defines a linearrelationship between measured ICRR (a “pure” measurement, M_(R)/M_(i),and with no predictive component) and predicted ICRR (a “pure”prediction, with no measurement component, but that accounts for anyspatial effects that may have resulted from changes in plantconfiguration or core conditions between measurements M_(R) and M_(i)).

After collecting multiple ICRR measurements, measured ICRR can becompared to the predicted ICRR at each state point. It is then possibleto quantify a global reactivity bias by determining the uniformreactivity adjustment to the predicted ICRR at each state point thatresults in ideal behavior, which is defined as a linear fit and ay-intercept of zero when performing a linear fit of measured ICRR versuspredicted ICRR. Fundamentally, the prediction is adjusted to matchmeasurement and the adjustment is used to correct the predictions forfuture evolutions (e.g., final approach to criticality).

Recognizing that (1/M) theory is practically represented by monitoringchanges in the measured neutron detector response from a baseline orreference condition, Equation (1) is a relationship familiar to nuclearreactor operators.M _(R)*(1−k _(R))∝M _(i)*(1−k _(i))  (1)

wherein, M_(R) and M_(i) are neutron detector responses at the referencestate point condition and a subsequent state point condition i,respectively, and k_(R) and k_(i) are the K_(eff) values at thereference state point condition and a subsequent state point conditioni, respectively.

Re-arrangement of terms yields a new Equation (2).

$\begin{matrix}{\frac{M_{R}}{M_{i}} \propto \frac{1 - k_{i}}{1 - k_{R}}} & (2)\end{matrix}$In this form, the left side of the equation is now only the ratio ofmeasured count rates (“raw”, or not-spatially corrected, measured ICRR,I_(M), i). The right side of the equation is comprised of coreeigenvalues that can be predicted by nuclear design calculations(predicted ICRR, I_(P), i) that take into account spatial effectsresulting from changes in control rod positions or primary systemconditions at the time of measurement. This separation of measurementfrom prediction is desirable in order to eliminate the potential formasking effects. In simplified form:I _(M,i) ∝I _(P,i)  (3)

The true regression of Equation (3) can be written as:I _(M)=β₁ *I _(P)+β₀  (4)The resultant estimate of the true regression, Equation (5), can be usedas a basis for core design validation prior to at-power operation of theplant; specifically, incremental and total measured changes in ICRR canbe compared to design prediction while the reactor is shutdown. Theresults evaluation is not subject to masking effects, andmeasured-to-predicted agreement (within pre-defined tolerance limits)demonstrates that the core is behaving as designed.Î _(M) =m*I _(P) +b  (5)Ideally, the as-built measured core is identical to the as-designedpredicted core, so that β₁ equals one and β₀ equals zero in Equation(4). However, in practice, this is not likely to be the case; somenon-trivial differences will likely be present in the line fit ofmeasured vs. predicted ICRR response. Regardless of the cause, it isespecially useful to quantify systematic reactivity bias so that it canbe used for criticality forecasting and monitoring purposes.

Returning to Equation (2), redefining the reference neutron detectormeasurement as a normalization constant (C) and rearrangement of termsyields the following:

$\begin{matrix}{M_{i} \propto \left\lbrack {C \cdot \frac{1 - k_{R}}{1 - k_{i}}} \right\rbrack} & (6)\end{matrix}$Equation (6) can be simplified and presented as a true regression bycombining the normalization constant and predictive terms into apredicted detector response at state point i (P_(i)) that also accountsfor spatial effects as explained previously:M _(i)=β₁ *P _(i)+β₀  (7)To quantify the global bias, the set of neutron detector measurementswill be fit versus their corresponding predicted values. The resultantestimate of the true regression is defined in Equation (8).{circumflex over (M)} _(i) =m*P _(i) +b  (8)

In an ideal situation, the y-intercept of the measured vs. predictedneutron detector response is zero. Assuming the regression estimate islinear and the data points are tightly fit, the globalmeasured-to-predicted reactivity bias can be estimated by determiningthe amount of reactivity adjustment required to drive the y-intercept(b) to zero for the line fit defined in Equation (8). The uniformreactivity adjustment across all state points (imparted via changes inthe P_(i) values) that produces a line fit with a y-intercept (b) ofzero is the estimated core reactivity bias.{circumflex over (M)} _(i) ={acute over (m)}*{acute over (P)} _(i)  (9)

Accordingly, the disclosed concept utilizes a direct comparison of rawsubcritical neutron flux measurements with corresponding predictions ateach state point condition. This differs from prior power reactorphysics testing methodologies, which require correction of themeasurement data prior to results evaluation; the benefit of thismethod, in employing complete separation of measurements andpredictions, is the prevention of masking effects (i.e., elimination ofinterdependency between measurement and prediction).

Additionally, the disclosed concept utilizes regression statistics ofraw neutron detector measurements to corresponding predictions, andquantitative measured-to-predicted criteria on such, to detect variouscore anomalies while the plant is in a subcritical condition and priorto the plant achieving criticality. The benefit of this approach is thatit provides an added measure of safety since anomalous core conditionscan be detected during hot standby testing and can be anticipated duringthe final approach to criticality.

Furthermore, the disclosed concept utilizes a method of determining thereactivity bias between the predicted core and actual core bydetermining the uniform analytical reactivity adjustment (systematicglobal reactivity bias) required to reconcile the measured neutron fluxdata with predictions. This differs from previous power reactor physicstest methodologies, for which the reactivity difference is determinedbased on measured reactivity at critical reactor conditions. The benefitof this approach is that it provides a way to identify anomalousreactivity indication/behavior in the subcritical state as a means ofproviding reactivity management guidance and/or accident prevention.Also, this method directly provides a reactivity bias offset on thepredictive model used in the plant safety analysis.

Application of this method requires neutron detector measurements andcorresponding core condition predictions that are provided by existingcore design codes and account for the subcritical neutron fluxdistribution. The basic uses of this method are to monitor and projectthe subcritical state of the core. Associated applications includemonitoring of negative reactivity conditions or shutdown margin, andforecasting of estimated critical conditions prior to plant startup. Themethod amounts to Subcritical Physics Testing, which integrates themonitoring and forecasting function to ultimately execute a series ofmeasured-to-predicted comparisons to confirm the as-built core isoperating consistent with design following refueling; results that couldonly previously been achieved during low power testing after the reactorwent critical.

A key piece of information needed for the safe and efficient operationof a subcritical reactor core is the negative reactivity of the core;that is, the amount that the core is subcritical, also known as theshutdown margin. Prior to development of the methodology describedherein, this information has only been inferred, and not directlymeasured.

The basic uses of this method are to project and monitor the negativereactivity of a subcritical core for any static configuration ofinterest, i.e., a steady-state combination of control rod position andprimary system conditions, through the use of neutron detector signalmeasurements and advanced subcritical core predictions. A series ofsubcritical measured-to-predicted comparisons during plant startup formsthe basis for the integrated application of this methodology, i.e., themeasured-to-predicted comparisons are performed at a number ofsteady-state subcritical conditions, each of which is referred to as astate point.

This method is performed at static and subcritical conditions (vs. thedynamic and critical conditions for traditional low power physicstesting). This method is revolutionary in that it is not just anextension of the steps performed during low power physics testing.However, this method achieves the same objective as low power physicstesting; following refueling and prior to returning to normal operation,testing is performed to determine if the operating characteristics ofthe core are consistent with design predictions as a means to ensure thecore can be operated as designed.

While achieving the same objective as low power physics testing,performing this method yields inherent safety, human performance, andtest performance benefits over low power physics testing. Performingmeasurements at static and subcritical conditions inherently enhancesplant safety and reactivity management. This method is seamlesslyintegrated into routine plant startup activities as opposed tonecessitating infrequently performed tests and evolutions and specialtest exceptions to plant operations, which improves test reliability andhuman performance. Therefore, this method-based core design verificationoffers broad benefits for essentially any plant type.

It is to be appreciated that methods as described herein can be carriedout by a processor or processing device of a computer system or by othermeans of carrying out the function. Thus, a processor with the necessaryinstructions programmed directly therein or on a machine readable mediumaccessed thereby for carrying out such a method or element of a methodforms a means for carrying out the method or element of a method.Furthermore, an element described herein of an apparatus embodiment isan example of a means for carrying out the function performed by theelement for the purpose of carrying out the invention.

While specific embodiments of the disclosed concept have been describedin detail, it will be appreciated by those skilled in the art thatvarious modifications and alternatives to those details could bedeveloped in light of the overall teachings of the disclosure.Accordingly, the particular embodiments disclosed are meant to beillustrative only and not limiting as to the scope of the disclosedconcept which is to be given the full breadth of the appended claims andany and all equivalents thereof.

What is claimed is:
 1. A method of determining a global core reactivitybias for a nuclear reactor core and bringing the nuclear reactor core toa critical reactor state, the method comprising: predicting acombination of parameters expected to yield the critical reactor stateof the nuclear reactor core, wherein the parameters comprise control rodposition, soluble boron concentration, and coolant temperature;operating a nuclear reactor at a first subcritical state; measuring,using a source range detector, a first measured neutron flux value whilethe nuclear reactor is operating at the first subcritical state;adjusting the nuclear reactor to operate at a second subcritical stateby repositioning at least one control rod of the nuclear reactor;measuring, using the source range detector, a second measured neutronflux value while the nuclear reactor is operating at the secondsubcritical state; predicting a first spatially-corrected neutron fluxvalue for the first subcritical state and a second spatially-correctedneutron flux value for the second subcritical state; comparing each ofthe measured neutron flux values with the correspondingspatially-corrected neutron flux values to determine the globalreactivity bias; wherein a spatial correction factor is not applied tothe measured neutron flux values; updating the predicted combination ofparameters by adjusting at least one of the parameters according to theglobal reactivity bias; and bringing the nuclear reactor core to thecritical reactor state using the updated combination of parameters. 2.The method of claim 1, further comprising performing a regressionanalysis to determine a relationship between the measured neutron fluxvalues and the corresponding spatially-corrected neutron flux values todetermine the global reactivity bias; wherein the determined globalreactivity bias is used to detect an anomaly associated with the nuclearreactor core without operating the reactor at a critical state.
 3. Themethod of claim 1, wherein the first subcritical state and the secondsubcritical state are steady-state conditions.
 4. The method of claim 1wherein the predicted combination of parameters are updated withoutoperating the nuclear reactor at the critical reactor state.
 5. Themethod of claim 1, wherein operating the reactor at the firstsubcritical state occurs after an initial construction of the nuclearreactor.
 6. The method of claim 1, wherein operating the nuclear reactorat the first subcritical state occurs after a refueling of the nuclearreactor.
 7. The method of claim 2, wherein the anomaly associated withthe nuclear reactor core is an anomalous reactivity behavior.
 8. Aprocessing device programmed to carry out the method of claim
 1. 9. Amachine readable medium comprising instructions for carrying out themethod of claim 1.